A014529: Examples of polygons of maximum area made from n equilateral triangles with sides s_k such that gcd(s_1,s_2,...,s_k)=1. Converted from illustration in Ian Stewart, Die unscheinbare Schwester der goldenen Zahl, Spektrum der Wissenschaft, Dossier 02/2003: Mathematische Unterhaltungen II, 55-57. Hugo Pfoertner, 2017-08-17 Areas are given relative to the size of a triangle with sides=1. a(1) = 1 * / \ *---* a(2) = 2 *---* / \ / *---* a(3) = 3 *---* / \ / \ *---*---* a(4) = 7 *---* / \ / \ *---*---* \ / + + \ / * a(5) = 11 *---* / \ / \ *---*---* \ / \ + + + \ / \ *---+---* a(6) = 20 *---*---+---+---* / \ / \ / *---*---* + \ / \ / + + + + \ / \ / *---+---* a(7) = 36 * / \ + + / \ + + / \ + + / \ *---*---+---+---* / \ / \ / *---*---* + \ / \ / + + + + \ / \ / *---+---* a(8) = 71 *---+---* / \ / \ + + + + / \ / \ + *---+---* / \ / \ + + + + / \ / \ *---+---+---+---* + \ / \ + *---+---+---* \ / \ / + + + + \ / \ / + + + + \ / \ / *---+---+---* a(9) = 146 *---+---+---*---+---+---+---* / \ / \ / \ + + + + + + / \ / \ / \ + + + + + + / \ / \ / \ *---+---+---*---+---+---* + + \ / \ / \ + *---*---+---+---+---* \ / \ / + + + + \ / \ / + + + + \ / \ / + + + + \ / \ / + + + + \ / \ / *---+---+---+---+---* a(10) = 260 *---+---+---+---* / \ / \ + + + + / \ / \ + + + + / \ / \ + + + + / \ / \ + *---+---+---+---* / \ / \ + + + + / \ / \ + + + + / \ / \ + + + + / \ / \ *---+---+---+---+---+---+---*---* + \ / \ / \ + *---*---+---+---+---+---* \ / \ / + + + + \ / \ / + + + + \ / \ / + + + + \ / \ / + + + + \ / \ / + + + + \ / \ / *---+---+---+---+---+---* a(11) = 495 *---+---+---+---+---+---+---+---* / \ / \ + + + + / \ / \ + + + + / \ / \ + + + + / \ / \ + + + + / \ / \ *---+---+---+---+---* + + / \ / \ / \ + + + + + + / \ / \ / \ + + + + + + / \ / \ / \ + + *---+---+---*---+---+---+---+---+---+---+---* / \ / \ / + + + + + / \ / \ / + *---+---* + / \ / \ / + + + + + / \ / \ / *---+---+---+---+---+---+---* + + \ / \ / + + + + \ / \ / + + + + \ / \ / + + + + \ / \ / + + + + \ / \ / + + + + \ / \ / + + + + \ / \ / *---+---+---+---+---+---+---+---+---*